If you're planting seeds, you can sow them in fall or spring; spring seeds need to be scarified. If you're planting bittersweet from the nursery, I would recommend early spring. Be sure to go to the extra trouble to find American bittersweet; the Chinese bittersweet is extremely invasive in some areas. You can google "where to buy American bittersweet" to find sources near you. Here is another article you might find interesting: https://www.gardeningknowhow.com/ornamental/vines/bittersweet/growing-bittersweet-vines.htm